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- 학술저널
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- 원광대학교 기초자연과학연구소 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS ANNALS OF FUZZY MATHEMATICS AND INFORMATICS 제14권 제5호
- 발행연도
- 2017.11
- 수록면
- 445 - 461 (17page)
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In this paper, we consider the $L-$generalized filters and $L-$generalized nets on the non empty universal set $X$ to be a natural generalization of the crisp generalized filters and the crisp generalized nets respectively. In each the crisp and $L-$generalized cases, the extended and restricted filters (nets) will be obtained respectively. The construction of convergence to limit points of the crisp generalized and $L-$generalized filters (nets) will be studied respectively. We also show that any crisp generalized net on the set $X$ associates a unique $L-$generalized net on $X,$ and in general the converse is not true. In addition to that we also show that for any given $L-$generalized filter there exists the $L-$generalized net, and the vice-versa is true. Finally, the relations between the convergence of the $L-$generalized filters and the $L-$generalized nets will be outlined. Moreover, to support these concepts and relations, the construction of some examples in all sections of paper will be studied.
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참고문헌 (23)
참고문헌 신청
N. Bourbaki / 1940 / General Topologey
N. Bourbaki / 1989 / Element of Mathematics General topology / Springer-Verlag
R. Baskaran / 2011 / Generalized Nets in Generalized Topological Spaces / Journal of Advanced Research in Pure Mathematics :1~7
C. L. Chang / 1968 / Fuzzy topological spaces / J. Math. Anal. Appl 24:182~190
G. Choqet / 1947 / Sur les notions de lter et grill / Comptes Rendus Acad. Sci. Paris 224:171~173
N. Bourbaki / 1989 / Element of Mathematics General topology / Springer-Verlag
R. Baskaran / 2011 / Generalized Nets in Generalized Topological Spaces / Journal of Advanced Research in Pure Mathematics :1~7
C. L. Chang / 1968 / Fuzzy topological spaces / J. Math. Anal. Appl 24:182~190
G. Choqet / 1947 / Sur les notions de lter et grill / Comptes Rendus Acad. Sci. Paris 224:171~173
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